Problem: Alexandra paid $\$7$ to park her car for $3$ hours at the parking garage. The garage charges a constant hourly parking rate. Write an equation that shows the relationship between $p$, the number of hours parked, and $c$, the cost in dollars.
Answer: Let's find the constant of proportionality. In the proportional relationship between $p$, the number of hours parked, and $c$, the cost in dollars, one constant of proportionality is the cost per hour. It is the number we multiply by the number of hours to get the total cost. $p\,\times\, ?=c$ $\begin{aligned} p\,\times\, {?}&=c \\\\ {?}&=\dfrac{c}{p} \\\\ &={\dfrac{7}{3}} \end{aligned}$ The constant of proportionality is ${\dfrac{7}{3}}$. This means we can multiply ${\dfrac{7}{3}}$ by the number of hours to get the total cost. Now, let's write the equation: $\begin{aligned} \text{total cost}&={\text{cost per hour}}\times\text{number of hours} \\\\ c&={\dfrac{7}{3}}p \end{aligned}$ One correct equation is: $c = \dfrac73p$